Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/16

 6

Alo the differences of the paces, which are decribed in equal differences of the times, decreae in the ame geometrical progreion.

The pace decribed by the body is the difference of two paces, whereof one is as the time taken from the beginning of the decent, and the other as the velocity; which [paces] alo at the beginning of the decent are equal among themelve.

Suppoing the force of gravity in any imilar medium to be uniform, and to tend perpendicular to the plane of the horizon; to define the motion of projectile therein, which uffers reiŧance proportional to its velocity.

Let the projectile go from any place D in the direction of any right line DP, and let its velocity at the beginning of the motion be expounded by the length DP. From the point P let fall the perpendicular PC on the horizontal line DC, and cut DC in A, o that DA may be to AC as the reitance of the medium ariing from its motion upwards at the beginning, to the force of gravity: or (which comes to the ame) o that the rectangle under DA and DP may be to that under AC and CP, as the whole reitance at the beginning of the motion to the force of gravity. With the aymptotes DC, CP decribe any Hyperbola GTBS cutting the perpendiculars DG, AB in G and B; compleat the parallelogram DGKC, and let its ide GK cut AB in Q. Take a line N in the ame ratio to QB as DC is in to CP; and from any point R of the right line DC, erect RT perpendicular to it, meeting the Hyperbola in T, and the right: lines EH, GK, DP in I, t and V; in that perpendicular